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Coexistence in a random growth model with competition

Research output: Contribution to journalJournal article

Unpublished
<mark>Journal publication date</mark>8/07/2019
<mark>Journal</mark>arxiv.org
Number of pages14
Publication statusUnpublished
Original languageEnglish

Abstract

We consider a variation of the Hastings-Levitov model HL(0) for random growth in which the growing cluster consists of two competing regions. We allow the size of successive particles to depend both on the region in which the particle is attached, and the harmonic measure carried by that region. We identify conditions under which one can ensure coexistence of both regions. In particular, we consider whether it is possible for the process giving the relative harmonic measures of the regions to converge to a non-trivial ergodic limit.

Bibliographic note

14 Pages, 1 figure